There is however some studies which focused on the short run basis of PPP. Chowdhry, Roll & Xia (2004) find that "relative PPP holds well in the short run in both single-country-pair OLS regressions and a pooled system regression" and that their evidence "for short-run relative PPP is unlikely to be driven by missing world factors or by real effects of inflation". Further, "our results complement the findings from the long-run PPP tests, and help resolve the PPP puzzle in the short run". They also have an evidence that "relative purchasing power parity holds quite well in the short run when inflation is extracted from stock prices". "For small differences in annual inflation between the United States and the country concerned, the correlation between relative inflation and depreciation in each of the years seems low. Relative PPP appears to "hold more closely for countries experiencing relatively high inflation" (Taylor & Taylor, 2004); "Finally, the IIRE is operative in both the short and long run in response to changes in the domestic price level" (Elwood & Fields, 1998). Based on those results, Click (1996), as mentioned by Fujiki & Kitamura in 2004 concludes that in "the time-series dimension, using the random-effects model, purchasing power parity holds, conditional upon the Balassa-Samuelson effect." Chapter 18 - Exchange Rate Theories discusses the favorable effect of PPP in the short run over long run. "PPP holds even in the short run within some blocks of nations"(Koedijk, Schotman and Van Dijk, 1998 quoted in Aggarwal & Simmon, 2002). "Short-run deviations from PPP are large and volatile" due to "financial factors such as changes in portfolio preferences, short-term asset price bubbles, and monetary shocks" (Rogoff, 1996).
The following references could also provide evidences of PPP in the short run.
CUMBY, ROBERT AND HUIZINGA, JOHN. "The Predictability of Real Exchange Rate
Changes in the Short and Long Run." Nat. Bureau Econ. Res. Working paper 3468, Oct. 1990.
Darby, Michael R. 1983. "Movements in Purchasing Power Parity: The Short and Long Runs,"
In The international transmission of inflation. Eds.: MICHAEL R. DARBY AND JAMES R. LOTHIAN ET AL. Chicago: U. of Chicago Press, Chicago, 1983, pp. 462-77.
Dornbusch, Rudiger. Exchange Rate Economics: Where Do We Stand,. Brookings Paper on
Economic Activity, 1, 1980, pp.143-85.
Dornbusch, Rudiger and Paul Krugman. 1976. "Flexible Exchange Rates in the Short Run."
Brookings Papers on Economic Activity. 1:3, pp. 537- 75
Dorodian, Khosrow; Jung, Chulho; Boyd, Roy. .Testing the Law of One Price Under the Fixed
And Flexible Exchange Rate System,. Applied Economics Letters, 6, 1999, pp. 613-6.
Frankel, Jeffrey A., (1976), "A Monetary Approach to the Exchange Rate," Scandinavian Journal of Economics, 78 (No. 2), pp. 200-224.
Frenkel, J. A. .Purchasing Power Parity: Doctrinal Perspective and Evidence from the 1920s,.
Journal of International Economics, 8,